Theoretical antiferromagnetism of ordered face-centered cubic Cr-Ni alloys

Contrary to prior calculations, the Ni-rich ordered structures of the Cr-Ni alloy system are found to be antiferromagnetic under semilocal density-functional theory. The optimization of local magnetic moments significantly increases the driving force for the formation of ${\mathrm{CrNi}}_2$, the only experimentally observed intermetallic phase. This structure's ab initio magnetism appears well described by a Heisenberg Hamiltonian with longitudinal spin fluctuations; itinerant Cr moments are induced only by the strength of exchange interactions. The role of magnetism at temperature is less clear and several scenarios are considered based on a review of experimental literature, specifically a failure of the theory, the existence of an overlooked magnetic phase transition, and the coupling of antiferromagnetism to chemical ordering. Implications for related commercial and high-entropy alloys are discussed for each case.

Figure 1

(a) The conventional unit cell of ${\mathrm{CrNi}}_2$. Dashed lines and coordinate axes indicate the conventional fcc unit cell. (b) Proposed AFM ground state of ${\mathrm{CrNi}}_2$, drawn on the same structure. Arbitrarily oriented “up” and “down” Cr moments are respectively represented using $•$ and $\circ$ markers. The actual tiling supercell is larger and an extension of the central $\left(\overline{1}10\right)$ plane is included to fully depict the ordering.

Figure 2

Calculated formation energies of various orderings discussed in the text as a function of composition. Annotations provide the prototype of each structure, with markers indicating the type of simulation cell and converged magnetic order. (A “unit cell” may be primitive or conventional.) The dotted and solid lines represent the convex hulls of stable structures based, respectively, on nonmagnetic and magnetic ${\mathrm{CrNi}}_2$.

Figure 3

Proposed AFM ground states for the (a) ${\mathrm{Al}}_3\mathrm{Ti}$-type and (b) ${\mathrm{MnCu}}_3$-type orderings of ${\mathrm{CrNi}}_3$, illustrated in the manner of Fig. 1. The perspective of (b) is along [001], in which Cr moments are AFM. Atomic sites are drawn with different sizes to illustrate alternating (001) and (002) planes. While ${\mathrm{MnCu}}_3$-type order is electronically more favorable, exchange interactions render ${\mathrm{Al}}_3\mathrm{Ti}$-type order lower energy, although neither is expected to be stable.

Figure 4

(a)–(c) Open circles: DFT energies of spin spirals representing modulations of the AFM ground state along the reciprocal lattice vectors of ${\mathrm{CrNi}}_2$, as indicated with fractional coordinates—the structure in Fig. 1 corresponds to $\left[q_1{q}_2{q}_3\right]=\left[\frac{1}{2}00\right]$. Solid lines: Equivalent values determined using Eq. (1) and Table 2. (d)–(f) As above, relaxed Cr moments from the same calculations and minimum energy values according to the effective Hamiltonian. (g) The energies of all considered spin spirals, as determined from the Hamiltonian vs as calculated with DFT. (h) Energy contribution from the longitudinal term of Eq. (1) as a function of local moment.